I am sorry for this delayed reply to your gardening question as we are transitioning to a new Q&A system. I hope this reply is not too late to be of help.
Your options are to either dig up the vines to get rid of them or to wipe a product containing glyphosate on the foliage on the vine, taking care to not get it on desirable plants.
Thanks for the question. Please stop in again soon!
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